When the lengths of two opposite sides of a square garden

Question

When the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. What was the area of the original square garden?

(1) The area of the new garden was 80 percent of the area of the original square garden
(2) x = 4

(1) The area of the new garden was 80 percent of the area of the original square garden
(2) x = 4

Bunuel · Answer

When the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. What was the area of the original square garden?

(1) The area of the new garden was 80 percent of the area of the original square garden
(2) x = 4

Let the side of the original square be  a . We are given that the area of the new garden was (a - x)(a + x) = a^2 - x^2 = 64.

We want to find the area of the original square, so the value of a^2.

(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a^2 --> a^2 = 80. Sufficient.

(2) x = 4 --> a^2 - 4^2 = 64 --> a^2 = 80. Sufficient.

Answer: D.

Hope it's clear.

rajmegaurav · Answer

Bunuel - How do we know that the reduced figure is a rectangle. It might even be a parallelogram where the opposite sides of the square are increased in opposite direction and the other opposite sides are reduced in the opposite direction.

Hope I am able to explain the situation :roll:

manpreetsingh86 · Answer

hi, because each internal angle of the square is 90, therefore the new figure will also have the same internal angle of 90 degrees each, that is why the new figure is rectangle and not a parallelogram.

sahilvijay · Answer

A initial area and y be original side
AreaA y^2
(y+x)(y-x)=64
1) New area is 0.8 of A
64=0.8A
Sufficient

2) x=4

(y+x)(y-x)=64
Then y can be calculated

Therefore sufficient.

D is answer

Sent from my iPhone using GMAT Club Forum

ramlala · Answer

Original square garden area = A = l * l = ?
we have new square garden area = 64

Sentence -1 The area of the new garden was 80 percent of the area of the original square garden
64 = 80% A
We can get value of A -  Sufficient

Sentence -2 x = 4
We already have (l+x) (l-x) = 64
We can get value of l * l -  Sufficient

ANS D

v12345 · Answer

Let original side be s.
Old area = s*s
New area = (s-x)(s+x) =  s^2 - x^2  = 64

(1) The area of the new garden was 80 percent of the area of the original square garden
 0.8 s^2 = 64 
We can get Area . Sufficient.

(2) x = 4 . Sufficient.
 s^2 - 4^2  = 64
 s^2 = 80

Hence, OA is (D).

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When the lengths of two opposite sides of a square garden

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